Asymmetric information scrambling and eigenstate thermalization in inhomogeneous XXZ spin chains

Abstract:Deterministic spatial inhomogeneity has become increasingly relevant in experimentally engineered quantum many-body systems, where interaction gradients can strongly influence nonequilibrium dynamics. Motivated by this, we investigate out-of-time-ordered correlators (OTOCs) and their connection to the eigenstate thermalization hypothesis (ETH) in inhomogeneous XXZ spin chains. Using a deterministic spatially varying interaction profile, we show that finite interaction gradients ($\delta>0$) induce a pronounced left--right asymmetry in information scrambling, as quantified by OTOCs. This asymmetry persists even when the system exhibits spectral signatures of quantum chaos, with operators on the strongly interacting side exhibiting suppressed scrambling. To elucidate the origin of the asymmetric finite-size long-time saturation value of OTOCs, we employ two complementary approaches. First, we analyze the diagonal matrix elements of the OTOC observables in the energy eigenbasis within the ETH framework. Second, we derive an analytical expression for the finite-size saturation value based on the overlap between the Hamiltonian and the OTOC observables, which explicitly incorporates the spatial interaction profile. The analytical prediction is fully consistent with the numerical results and provides a microscopic explanation for how deterministic interaction gradients generate the observed asymmetry in the long-time saturation of OTOCs.

arXiv:2607.25496 [quant-ph]

(or arXiv:2607.25496v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.25496 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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